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Aberration of the Green's function estimator in hybridization expansion continuoustime quantum Monte Carlo
by Andreas Hausoel, Markus Wallerberger, Josef Kaufmann, Karsten Held, Giorgio Sangiovanni
Submission summary
Authors (as Contributors):  Andreas Hausoel 
Submission information  

Arxiv Link:  https://arxiv.org/abs/2211.06266v1 (pdf) 
Code repository:  https://github.com/w2dynamics 
Date submitted:  20221128 17:01 
Submitted by:  Hausoel, Andreas 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
We describe an aberration of the resampling estimator for the Green's function customarily used in hybridization expansion continuoustime quantum Monte Carlo. It occurs due to Pauli principle constraints in calculations of Anderson impurity models with baths consisting of a discrete energy spectrum. We identify the missing Feynman diagrams, characterize the affected models and discuss implications as well as solutions. This issue does not occur when using worm sampling or in the presence of continuous baths. However certain energy spectra can be inherently close to a discrete limit, and we explain why autocorrelation times can become very large in these cases.
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Reports on this Submission
Anonymous Report 2 on 2023118 (Contributed Report)
Strengths
1 The paper “Aberration of the Green's function estimator in hybridization expansion continuoustime quantum Monte Carlo” by Andreas Hausoel, Markus Wallerberger, Josef Kaufmann, Karsten Held, Giorgio Sangiovanni presents specify the problem in the standard CTHYB estimator of the Green's function, and identify the origin, which is related to the Pauli principle constraints in the Anderson impurity model. They suggest an alternative Green's function estimator, which works well in comparison with the exact diagonalization.
2 The underlying idea for the method is well described.
3 Numerical results support their claim.
Weaknesses
1 There was no indication of how V, δ, etc. should be set quantitatively, which might be depend on the other parameters.
2No discussion existed on how this method affects the selfconsistency calculations when CTQMC is used as an impurity problem for DMFT.
3The specific input to reproduce the numerical results given in the manuscript is not on the Github. It would be very helpful for readers if the authors provide the readytorun input. Since there seems only DMFT examples exists currently.
Report
Overall, this is a wellwritten paper that makes an important contribution to the field. I recommend that it be accepted for publication in SciPost physics with the following major revisions.
Requested changes
[Major]
1 As shown in the Figures 911, the behavior of the critical diagrams contribution to G(\tau) is quite different for the parameters such as V, \delta and \beta. It would be of interest, how the validity for these parameters changes in the AIM.
2 I understand that it is an improvement in the Green's function obtained by CTHYB in the hightemperature region, but it is a hindrance to systematic analysis on the high energy region to the low energy region, which is the strength of CTHYB, and it seems one need to turn on and off this estimator as approaching to the lowenergy region. Do the authors have any solutions regarding this point? At least a comment on this point is needed.
3 Also, it would be very helpful for the readers to give the affect of the selfconsistency calculations when this CTQMC is used as an impurity problem for DMFT.
[Minor]
3 On page 18, authors refer to Fig. 3 (a), which is not exists.
Anonymous Report 1 on 202314 (Invited Report)
Strengths
1  The work of Andreas Hausoel et al. uncovers a possible deviation of the estimation of the Green's function usually used with hybridization expansion CTQMC. The sampling of the Green's function is vital in order to understand the many body physics of the Anderson impurity model and so to unveil methodological limitations that can occur by using one very common method as CTHYB is very important.
2 The methodology is well introduced and explain in the text.
3  The numerical results are convincing and the comparison with the worm sampling and exact diagonalization well illustrated.
Weaknesses
1  The Anderson impurity model is often used in dynamical mean field theory in order to solve the Hubbard model. In this work it is missing a discussion on the implication of this aberration found by the authors. In light of the results presented here I feel that some published work could be put under scrutiny in order to see if their results are correct.
2  The bibliography is quite limited and I think the authors should add more references to it. There is no reference to the initial work of Anderson ( Anderson, P. W. (1961). "Localized Magnetic States in Metals". Phys. Rev. 124 (1): 41–53) and neither to the first works on the CTHYB (A.N. Rubtsov, A.I. Lichtenstein JETP Lett., 80 (2004), p. 61)
but more important a series of articles that can be impacted by these results.
Report
I believe that this work meets the general expectations and criteria to be published. Nevertheless I would recommend to enlarge the implications that this work have on previous works on the Anderson impurity model and on other works on the Dynamical mean field theory.
Requested changes
1  I would recommend to enlarge the implications that this work have on previous works on the Anderson impurity model and on other works on the Dynamical mean field theory.
2 I would recommend to extend the bibliography especially adding a series of articles that can be impacted by these results.
3On figure 7 I suggest to add yaxis label for both panels.
4On figure 9 I suggest to eliminate the xaxis label and ticks label for the first four rows. I also suggest to add yaxis label for all panels.
5On figure 10 I suggest to eliminate the xaxis label and ticks label for the first three rows. I also suggest to add yaxis label for all panels.
6On figure 12 I suggest to add the xaxis label on the last row. I also suggest to add yaxis label for all panels.
7 In which way the integrals are evaluated? Probably not but can the results change by using different methods of estimations of the integrals?